Some special bases of the 2-swap algebras


Abstract


We study the algebra \Sigma_n induced by the action of the symmetric group S_n on V^{\otimes n} when \dim V=2. Our main result is that the space of symmetric elements of \Sigma_n is linearly spanned by the involutions of S_n.

DOI Code: 10.1285/i15900932v45n1p39

Keywords: swap algebra; symmetric group; representations

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